Spiral/Elliptical Kinematics

Beena Meena Astro 8400 Cosmic Distance Ladder

15 Mpc to 200 Mpc

Upto 15 Mpc

Spirals

“The Essential Cosmic Perspective”, Bennett et al Elliptical: Faber-Jackson Relation

4/20/20 Beena Meena - Astro 8400 2 Galaxy Rotation: Basics

Km/sec

https://pages.uoregon.edu/jimbrau/BrauImNew/Chap24/6th/24_11Figure-F. jpg

4/20/20 Beena Meena - Astro 8400 3 Galaxy Rotation from HI (λ 21cm) line Credit: JRob’s prospectus Note: Line width needs to be corrected for inclination: Width/sin(i)

4/20/20 Beena Meena - Astro 8400 4 The Tully - Fisher Relation

“A new method of determining distance to ”, Tully, R.B; Fisher, J.R., A&A, 1977, A&A, 54, 661 Line width∝ (Brighter galaxies rotate faster)

4/20/20 Beena Meena - Astro 8400 5 Original Tully Fisher Relation (TFR) “A new method of determining distance to galaxies”, Tully, R.B; Fisher, J.R., A&A, 1977, A&A, 54, 661 • Photometric measurements (M81 & M101) : Cepheid distances

• Note: Absolute Magnitude M∝ d

• Radio observation: 91 m NRAO

• Apparent Mag. (m): Optical (B)

• Find Best fit: Calibration

• Apply to distant galaxies

4/20/20 Beena Meena - Astro 8400 6 TFR for distance measurement

1) Distance Modulus µ = m – M

ΔV(0): H1 line width corrected for inclination mpg : Photographic magnitude

Slope (⍺) Log(L) 2) Hubble Constant H0 = V/d Preliminary Value = 80 km s−1 Mpc−1

ΔV(0) 4/20/20 Beena Meena - Astro 8400 7 Progress: TF Relationship

• Moved on from visible to other bandpasses

• Tully Fisher Relation is tighter in I band

−1 −1 • H0 = 71 +/-7 km s Mpc

Sakai et al., ApJ 529, 698 (2000)

4/20/20 Beena Meena - Astro 8400 8 Advanced TF Relation (by Tully) Tully et al. , AJ , 2013, 146, 4

Cosmicflows2 • Cosmicflows3: 17,669 entries

• Photometry at 3.6 µm Observation: Spitzer Space Telescope

• Cepheid, Tip of the Red Giant Branch (TRGB), Type Ia supernova (SNIa): Distance Calibrations

−1 −1 • H0 = 76.2 +/-2.7 km s Mpc

4/20/20 Beena Meena - Astro 8400 9 More recent Results: • Lelli Federco et al., MNRAS,2019 484,3 • A const. M/L ratio breaks at Low Luminosity galaxies • Include gas mass so total mass = Stellar mass + gas (Baryonic mass) • Baryonic Tully –Fischer relation (from McGaugh et. al. 2000, 533,2 ) • Slope (⍺) = 3.85 ± 0.09

Sheii, J. R. et al., AAS 2020, 4,4 “Tully Fischer for southern galaxies with HIPASS and WISE” −1 −1 Hubble Const. H0 = 73.3 ± 1 km s Mpc

Range of Distance measurements: upto z = 1.4 Lorenzo et al., A&A,2010, 521,A27

4/20/20 Beena Meena - Astro 8400 10 Limitations & Source of Errors

• Does not consider mass from dark Matter: Halo(?)

• Constant M/L ratio for a range of luminosity

• Errors due to measurement of inclination (5% uncertainties in inclination amounts to 9% error in line width: cosmicflow2, Tully et al 2013)

• More: Uncertainties in measurement of

4/20/20 Beena Meena - Astro 8400 11 Elliptical Galaxies

• Prolate (Rugby ball) shape

• Generally composed of older, low-mass

• Minimal formation

• Hardly rotating: Can’t use Tully Fischer

• Stellar velocity dispersion M87: Wikipedia

4/20/20 Beena Meena - Astro 8400 12 Faber–Jackson relation

• Presented by astronomers Sandra M. “Velocity dispersions and mass-to-light ratios for elliptical galaxies”, Faber, S. M.; Jackson, R. E. Faber and Robert Earl Jackson in 1976 1976,ApJ, 204, 668

• Similar to TF L ∝ σˠ Velocity dispersion(σ) σ = Stellar velocity dispersion ˠ ∼ 4

4/20/20 Beena Meena - Astro 8400 13 Fundamental Plane (FP)

• To minimize the scatter in Faber Jackson

• Djorgovski, S.; Davis, Marc 1987 coined the term Fundamental Plane:

• (Lum)⍺(Radius)β(vel. dispersion)ˠ = Const.

• Any one of the three parameters may be Dn = Diameter measured at estimated from the other two. 20.75 mag per square arcsecond Dressler et al., 1987, ApJ 313, 42

4/20/20 Beena Meena - Astro 8400 14 (FP) (somewhat) Recent Results:

Ellipticals S0 Galaxies

Reduced Scattering from 25% (Dresseler et al. 1987) to 20% for each galaxy

Bernardi et al.,2002, AJ 123, 2159

4/20/20 Beena Meena - Astro 8400 15 Summary

• Distance Ladder Rung 5: Galaxy Kinematics Best within ≈ 200Mpc

• Spiral-> Tully Fisher : L ∝ (ΔV)⍺ ; ⍺ ∼ 3 to 4

• Elliptical -> Faber Jackson: L ∝ σˠ or Fundamental Plane

4/20/20 Beena Meena - Astro 8400 16 Thank you!

4/20/20 Beena Meena - Astro 8400 17